$\DeclareMathOperator\GL{GL}\DeclareMathOperator\SO{SO}$I know a little bit about complex representation theory of finite reductive groups as $\GL_n(q),\SO_n(q)$ etc via Deligne-Lusztig induction and so on. If I correctly understood, there's another geometric way to build the characters (at least in the $\GL_n$ case) via the so-called character sheaves. I've just have read very vaguely something about this and it seems to me strictly related to the same circle of idea which brings up Springer correspondence etc: I'd be particularly interested in the link between the twos.

Are there any book or introductory references which treat this construction? I'd be particularly interested just in the $\GL_n$ case and in a focus towards examples maybe. I tried to read the original articles by Lusztig but they are maybe a bit too general/ difficult for what I had in mind.